Finite Group Databasebeta

← C2×#20252333 #27080656

Subgroups — C2×#20252333 #27080656

Order 12032.

1938 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689677C211yesmaximal, characteristic
2#20252333C2116yesmaximal, direct product factor
3C2×#15689254C211yesmaximal, characteristic, complemented
4C2×#15689252C211yesmaximal, characteristic, complemented
5C2×#15689252C211yesmaximal, characteristic, complemented
6C2×#15689251C211yesmaximal, characteristic, complemented
7C2×#15689251C211yesmaximal, characteristic, complemented
8C2×C8×Dic94C211yesmaximal, characteristic, complemented
9C2×#15689247C211yesmaximal, characteristic, complemented
10C2×#15689148C211yesmaximal, characteristic
11C2×#15689148C211yesmaximal, characteristic
12C2×C4⋊C8×D47C211yesmaximal, characteristic
13C2×#15689080C211yesmaximal, characteristic
14C2×#15689077C211yesmaximal, characteristic
15C2×#15689075C211yesmaximal, characteristic
16C2×C47×#446C211yesmaximal, characteristic, complemented
17C22×#10625324C2211yescharacteristic
18C22×#10625324C2211yescharacteristic
19C22×C8×D47C2211yescharacteristic
20C22×C8×D47C2211yescharacteristic
21#15689677C418yes—
22#15689677C2218yes—
23C2×#13094023C411yescharacteristic
24C2×#13094022C411yescharacteristic
25C2×#13094014C411yescharacteristic
26C2×#13094014C411yescharacteristic
27C2×#13094004C411yescharacteristic
28C2×#13094002C411yescharacteristic
29C2×#13094002C411yescharacteristic
30C2×#13094000C411yescharacteristic
31C2×C4×Dic94C2211yescharacteristic
32C2×C4×Dic94C2211yescharacteristic
33C2×C4×Dic94C2211yescharacteristic
34C2×#13093981C2211yescharacteristic
35C2×#13093981C2211yescharacteristic
36C2×C42×D47C2211yescharacteristic
37#15689254C2218yescomplemented
38#15689252C2218yescomplemented
39#15689252C2218yescomplemented
40#15689251C2218yescomplemented
41#15689251C2218yescomplemented
42C8×Dic94C2218yescomplemented
43#15689247C2218yescomplemented
44#15689148C2218yes—
45#15689148C2218yes—
46C2×C4⋊(C47⋊C8)C2211yescharacteristic
47C2×C4⋊(C47⋊C8)C2211yescharacteristic
48C2×C4⋊(C47⋊C8)C2211yescharacteristic
49C2×Dic47⋊C8C2211yescharacteristic
50C2×Dic47⋊C8C2211yescharacteristic
51C2×Dic47⋊C8C2211yescharacteristic
52C2×Dic47⋊C8C2211yescharacteristic
53C2×Dic47⋊C8C2211yescharacteristic
54C2×Dic47⋊C8C2211yescharacteristic
55C4⋊C8×D47C2218yes—
56#15689080C2218yes—
57#15689077C2218yes—
58#15689075C2218yes—
59C2×#13093935C2211yescharacteristic
60C2×#13093935C2211yescharacteristic
61C2×#13093934C2211yescharacteristic
62C2×#13093934C2211yescharacteristic
63C2×C4×C47⋊C8C2211yescharacteristic
64C2×C8×Dic47C2211yescharacteristic
65C2×C8×Dic47C2211yescharacteristic
66C2×C8×Dic47C2211yescharacteristic
67C2×C8×Dic47C2211yescharacteristic
68C2×C4×Q8×C47C2211yescharacteristic
69C47×#446C2218yescomplemented
70C2×C4⋊C8×C47C2211yescharacteristic
71C2×C4⋊C8×C47C2211yescharacteristic
72C2×C4⋊C8×C47C2211yescharacteristic
73C2×#97×C47C2211yescharacteristic
74C2×#97×C47C2211yescharacteristic
75C2×C4×C8×C47C2211yescharacteristic
76C22×Dic94C2×C411yescharacteristic
77C22×Dic94C2×C411yescharacteristic
78C22×Dic94C2×C411yescharacteristic
79C22×C4×D47C2×C411yescharacteristic
80C22×C4×D47C2×C411yescharacteristic
81C22×C4×D47C2311yescharacteristic
82C2×#10625324—24no—
83C2×#10625324Q818yescomplemented
84C2×#10625324C2314yes—
85C2×#10625324C2314yes—
86C22×C47⋊C8C2311yescharacteristic
87C22×C47⋊C8C2311yescharacteristic
88C22×C47⋊C8C2311yescharacteristic
89C22×C47⋊C8C2311yescharacteristic
90C2×C8×D47—24no—
91C2×C8×D47—24no—
92C2×C8×D47C2314yes—
93C2×C8×D47C2314yes—
94#13094023C2×C418yes—
95#13094022C2×C418yes—
96#13094014C2×C418yes—
97#13094014C2×C418yes—
98#13094004C2×C418yes—
99#13094002C2×C418yes—
100#13094002C2×C418yes—
101#13094000C2×C418yes—
102C4×Dic94C2×C414yes—
103C4×Dic94C2×C414yes—
104C4×Dic94C2×C414yes—
105C4×Dic94C2314yes—
106C4×Dic94C2314yes—
107C4×Dic94C2314yes—
108#13093981C2×C414yes—
109#13093981C2×C414yes—
110#13093981C2314yes—
111#13093981C2314yes—
112C2×C4⋊Dic47C2×C411yescharacteristic
113C2×C4⋊Dic47C2×C411yescharacteristic
114C2×C4⋊Dic47C2×C411yescharacteristic
115C2×Dic47⋊C4C2×C411yescharacteristic
116C2×Dic47⋊C4C2×C411yescharacteristic
117C2×Dic47⋊C4C2×C411yescharacteristic
118C2×Dic47⋊C4C2×C411yescharacteristic
119C2×Dic47⋊C4C2×C411yescharacteristic
120C2×Dic47⋊C4C2×C411yescharacteristic
121C2×Dic47⋊C4C2×C411yescharacteristic
122C2×Dic47⋊C4C2×C411yescharacteristic
123C2×Dic47⋊C4C2×C411yescharacteristic
124C2×Dic47⋊C4C2×C411yescharacteristic
125C2×(C2×D47)⋊C4C2×C411yescharacteristic
126C2×(C2×D47)⋊C4C2×C411yescharacteristic
127C2×(C2×D47)⋊C4C2×C411yescharacteristic
128C2×(C2×D47)⋊C4C2×C411yescharacteristic
129C2×C4×Dic47C2×C411yescharacteristic
130C2×C4×Dic47C2×C411yescharacteristic
131C2×C4×Dic47C2311yescharacteristic
132C2×C4×Dic47C2311yescharacteristic
133C2×C4×Dic47C2311yescharacteristic
134C42×D47C2×C414yes—
135C42×D47C2314yes—
136C4⋊(C47⋊C8)C2314yes—
137C4⋊(C47⋊C8)C2314yes—
138C4⋊(C47⋊C8)C2314yes—
139Dic47⋊C8C2314yes—
140Dic47⋊C8C2314yes—
141Dic47⋊C8C2314yes—
142Dic47⋊C8C2314yes—
143Dic47⋊C8C2314yes—
144Dic47⋊C8C2314yes—
145#13093935C2314yes—
146#13093935C2314yes—
147#13093934C2314yes—
148#13093934C2314yes—
149C4×C47⋊C8C2314yes—
150C8×Dic47C2314yes—
151C8×Dic47C2314yes—
152C8×Dic47C2314yes—
153C8×Dic47C2314yes—
154C22×Q8×C47C2×C411yescharacteristic
155C22×C8×C47C2311yescharacteristic
156C22×C8×C47C2311yescharacteristic
157C22×C8×C47C2311yescharacteristic
158C22×C8×C47C2311yescharacteristic
159C4×Q8×C47C2×C414yes—
160C4×Q8×C47C2314yes—
161C2×C4⋊C4×C47C2×C411yescharacteristic
162C2×C4⋊C4×C47C2×C411yescharacteristic
163C2×C4⋊C4×C47C2×C411yescharacteristic
164C2×C42×C47C2311yescharacteristic
165C2×C42×C47C2311yescharacteristic
166C2×C42×C47C2311yescharacteristic
167C4⋊C8×C47C2314yes—
168C4⋊C8×C47C2314yes—
169C4⋊C8×C47C2314yes—
170#97×C47C2314yes—
171#97×C47C2314yes—
172C4×C8×C47C2314yes—
173C23×D47C22×C411yescharacteristic
174C2×Q8×C47—42no—
175C2×Q8×C47C22×C414yes—
176C22×C4×C47C22×C411yescharacteristic
177C22×C4×C47C22×C411yescharacteristic
178C22×C4×C47C22×C411yescharacteristic
179C22×C4×C47C22×C411yescharacteristic
180C22×C4×C47C22×C411yescharacteristic
181C22×C4×C47C22×C411yescharacteristic
182C22×C4×C47C2411yescharacteristic
183C22×Dic47C22×C411yescharacteristic
184C22×Dic47C22×C411yescharacteristic
185C22×Dic47C22×C411yescharacteristic
186C22×Dic47C22×C411yescharacteristic
187C22×Dic47C22×C411yescharacteristic
188C22×Dic47C22×C411yescharacteristic
189C22×Dic47C22×C411yescharacteristic
190C2×C4×D47—24no—
191C2×C4×D47—42no—
192C2×C4×D47C22×C414yes—
193C2×C4×D47C22×C414yes—
194C2×C4×D47C22×C412yes—
195C2×C4×D47C2×Q814yes—
196C2×C4×D47#4114yes—
197C2×C4×D47C2412yes—
198C2×Dic94—24no—
199C2×Dic94—24no—
200C2×Dic94—42no—
201C2×Dic94C22×C414yes—
202C2×Dic94C22×C414yes—
203C2×Dic94C22×C414yes—
204C2×C8×C47—22no—
205C2×C8×C47—22no—
206C2×C8×C47—22no—
207C2×C8×C47C2×Q814yes—
208C2×C8×C47C2412yes—
209C2×C8×C47C2412yes—
210C2×C8×C47C2412yes—
211C2×C8×C47C2412yes—
212C4⋊C4×C47C22×C414yes—
213C4⋊C4×C47C22×C414yes—
214C4⋊C4×C47C22×C414yes—
215C42×C47C22×C412yes—
216C42×C47C22×C412yes—
217C42×C47C22×C412yes—
218C42×C47C2412yes—
219C42×C47C2412yes—
220C42×C47C2412yes—
221(C2×D47)⋊C4C22×C414yes—
222(C2×D47)⋊C4C22×C414yes—
223(C2×D47)⋊C4C22×C414yes—
224(C2×D47)⋊C4C22×C414yes—
225C4⋊Dic47C22×C414yes—
226C4⋊Dic47C22×C414yes—
227C4⋊Dic47C22×C414yes—
228Dic47⋊C4C22×C414yes—
229Dic47⋊C4C22×C414yes—
230Dic47⋊C4C22×C414yes—
231Dic47⋊C4C22×C414yes—
232Dic47⋊C4C22×C414yes—
233Dic47⋊C4C22×C414yes—
234Dic47⋊C4C22×C414yes—
235Dic47⋊C4C22×C414yes—
236Dic47⋊C4C22×C414yes—
237Dic47⋊C4C22×C414yes—
238C4×Dic47C22×C412yes—
239C4×Dic47C22×C414yes—
240C4×Dic47C22×C414yes—
241C4×Dic47C22×C412yes—
242C4×Dic47C22×C412yes—
243C4×Dic47C2412yes—
244C4×Dic47C2412yes—
245C4×Dic47C2412yes—
246C2×C47⋊C8—22no—
247C2×C47⋊C8—22no—
248C2×C47⋊C8—22no—
249C2×C47⋊C8C2×Q814yes—
250C2×C47⋊C8C2412yes—
251C2×C47⋊C8C2412yes—
252C2×C47⋊C8C2412yes—
253C2×C47⋊C8C2412yes—
254#10625324—28no—
255#10625324C2×Q8116yescomplemented
256C8×D47—28no—
257C8×D47—28no—
258C23×C47C23×C411yescharacteristic
259C22×D47—22no—
260C22×D47—22no—
261C22×D47C4×Q814yes—
262C22×D47C23×C412yes—
263Q8×C47—44no—
264C2×C4×C47—22no—
265C2×C4×C47—22no—
266C2×C4×C47—22no—
267C2×C4×C47—22no—
268C2×C4×C47—22no—
269C2×C4×C47—22no—
270C2×C4×C47C23×C412yes—
271C2×C4×C47C23×C412yes—
272C2×C4×C47C23×C412yes—
273C2×C4×C47C23×C412yes—
274C2×C4×C47C23×C412yes—
275C2×C4×C47C23×C412yes—
276C2×C4×C47C23×C411yescharacteristic
277C2×C4×C47C22×Q812yes—
278C2×C4×C47C2×#4112yes—
279C2×C4×C47C2511yescharacteristic
280C2×Dic47—22no—
281C2×Dic47—22no—
282C2×Dic47—22no—
283C2×Dic47—22no—
284C2×Dic47—22no—
285C2×Dic47C4×Q814yes—
286C2×Dic47#13114yes—
287C2×Dic47C23×C412yes—
288C2×Dic47C23×C412yes—
289C2×Dic47C23×C412yes—
290C2×Dic47C23×C412yes—
291C2×Dic47C23×C412yes—
292C2×Dic47C23×C412yes—
293C2×Dic47C23×C412yes—
294C4×D47—28no—
295C4×D47—44no—
296C4×D47C4×Q818yes—
297C4×D47C22×Q814yes—
298C4×D47C2×#4114yes—
299Dic94—28no—
300Dic94—28no—
301Dic94—44no—
302C8×C47—22no—
303C8×C47—22no—
304C8×C47—22no—
305C8×C47C22×Q814yes—
306C47⋊C8—22no—
307C47⋊C8—22no—
308C47⋊C8—22no—
309C47⋊C8C22×Q814yes—
310C2×#2962—471nomaximal, Sylow
311C22×C47C2×C4×Q812yes—
312C22×C47C2×#13112yes—
313C22×C47#56812yes—
314C22×C47C24×C411yescharacteristic
315C2×D47—28no—
316C2×D47—22no—
317C2×D47—22no—
318C2×D47C2×C4×Q814yes—
319C4×C47—22no—
320C4×C47—22no—
321C4×C47—22no—
322C4×C47—22no—
323C4×C47—22no—
324C4×C47—22no—
325C4×C47C2×C4×Q812yes—
326C4×C47C23×Q811yescharacteristic
327C4×C47C22×#4111yescharacteristic
328Dic47—22no—
329Dic47—22no—
330Dic47—22no—
331Dic47—22no—
332Dic47—22no—
333Dic47C2×C4×Q814yes—
334Dic47C2×#13114yes—
335C2×#533—471no—
336#2962—4716no—
337C2×#446—471no—
338C2×#446—471no—
339C2×#446—471no—
340C2×#446—471no—
341C2×#446—471no—
342C2×#446D4711yescharacteristic, complemented
343C2×C8×Q8—471no—
344C2×C8×Q8—471no—
345C2×#424—471no—
346C2×#424—471no—
347C22×C4⋊C8—471no—
348C2×#405—471no—
349C2×#405—471no—
350C2×C4×M16—471no—
351C2×C47#296214yescomplemented
352C2×C47C22×C4×Q811yescharacteristic
353C2×C47C22×#13111yescharacteristic
354C2×C47C2×#56811yescharacteristic
355D47—24no—
356C22×M16—471no—
357C22×M16—471no—
358C23×C8—471no—
359C23×C8—471no—
360#533—478no—
361#533—478no—
362C2×C4⋊Q8—471no—
363C2×C4⋊Q8—471no—
364C2×#125—471no—
365C2×#125—471no—
366C2×C22⋊Q8—471no—
367C2×C22⋊Q8—471no—
368C2×C22⋊Q8—471no—
369C2×C22⋊Q8—471no—
370C2×C4×Q8—471no—
371C2×C4×Q8—471no—
372C2×C4×Q8—471no—
373C2×C4×Q8C2×D4711yescharacteristic
374C2×#117—471no—
375C2×#117—471no—
376C22×C42—471no—
377#446—478no—
378#446—478no—
379#446—478no—
380#446—478no—
381#446—478no—
382#446C2×D4718yescomplemented
383C8×Q8—478no—
384C8×Q8—478no—
385#424—478no—
386#424—478no—
387C2×C4⋊C8—471no—
388C2×C4⋊C8—471no—
389C2×C4⋊C8—471no—
390C2×C4⋊C8—471no—
391C2×C4⋊C8—471no—
392C2×C4⋊C8—471no—
393C2×C4⋊C8—471no—
394C2×C4⋊C8—471no—
395C2×C4⋊C8—471no—
396C2×C4⋊C8—478no—
397C2×C4⋊C8C2×D4711yescharacteristic
398C2×C4⋊C8C2×D4711yescharacteristic
399C2×C4⋊C8C2×D4711yescharacteristic
400#405—478no—
401#405—478no—
402C4×M16—478no—
403C2×#97—471no—
404C2×#97—471no—
405C2×#97—471no—
406C2×#97—471no—
407C2×#97C2×D4711yescharacteristic
408C2×#97C2×D4711yescharacteristic
409C2×C4×C8—471no—
410C2×C4×C8—471no—
411C2×C4×C8—471no—
412C2×C4×C8—471no—
413C2×C4×C8—471no—
414C2×C4×C8C2×D4711yescharacteristic
415C47C2×#296211yescharacteristic, complemented, Sylow
416C22×Q8—471no—
417C22×Q8—471no—
418C22×Q8—471no—
419C22×Q8C4×D4711yescharacteristic
420C23×C4—471no—
421C23×C4—471no—
422C23×C4—471no—
423C2×M16—478no—
424C2×M16—474no—
425C2×M16—474no—
426C2×M16—944no—
427C22×C8—471no—
428C22×C8—471no—
429C22×C8—471no—
430C22×C8—471no—
431C22×C8—474no—
432C22×C8—474no—
433C22×C8—944no—
434C22×C8—944no—
435C22×C8C22×D4711yescharacteristic
436C22×C8C22×D4711yescharacteristic
437C22×C8C22×D4711yescharacteristic
438C22×C8C22×D4711yescharacteristic
439C4⋊Q8—478no—
440C4⋊Q8—478no—
441#125—478no—
442#125—478no—
443C22⋊Q8—478no—
444C22⋊Q8—478no—
445C22⋊Q8—478no—
446C22⋊Q8—478no—
447C4×Q8—474no—
448C4×Q8—474no—
449C4×Q8—474no—
450C4×Q8—474no—
451C4×Q8—474no—
452C4×Q8—474no—
453C4×Q8C4×D4714yes—
454C4×Q8C22×D4714yes—
455#117—474no—
456#117—474no—
457#117—474no—
458#117—474no—
459C2×C4⋊C4—471no—
460C2×C4⋊C4—471no—
461C2×C4⋊C4—471no—
462C2×C4⋊C4—471no—
463C2×C4⋊C4—471no—
464C2×C4⋊C4—471no—
465C2×C4⋊C4—471no—
466C2×C4⋊C4—471no—
467C2×C4⋊C4—471no—
468C2×C4⋊C4—471no—
469C2×C4⋊C4—471no—
470C2×C4⋊C4—471no—
471C2×C4⋊C4—471no—
472C2×C4⋊C4C4×D4711yescharacteristic
473C2×C4⋊C4C4×D4711yescharacteristic
474C2×C4⋊C4C4×D4711yescharacteristic
475C2×C22⋊C4—471no—
476C2×C22⋊C4—471no—
477C2×C22⋊C4—471no—
478C2×C22⋊C4—471no—
479C2×C42—471no—
480C2×C42—471no—
481C2×C42—471no—
482C2×C42—471no—
483C2×C42—471no—
484C2×C42—474no—
485C2×C42—474no—
486C2×C42C22×D4711yescharacteristic
487C2×C42C22×D4711yescharacteristic
488C2×C42C22×D4711yescharacteristic
489C4⋊C8—474no—
490C4⋊C8—474no—
491C4⋊C8—474no—
492C4⋊C8—474no—
493C4⋊C8—474no—
494C4⋊C8—474no—
495C4⋊C8—474no—
496C4⋊C8—474no—
497C4⋊C8—474no—
498C4⋊C8C22×D4714yes—
499C4⋊C8C22×D4714yes—
500C4⋊C8C22×D4714yes—
501#97—474no—
502#97—474no—
503#97—474no—
504#97—474no—
505#97C22×D4714yes—
506#97C22×D4714yes—
507C4×C8—474no—
508C4×C8—474no—
509C4×C8—474no—
510C4×C8—474no—
511C4×C8—474no—
512C4×C8C22×D4714yes—
513C24—471no—
514C2×Q8—42no—
515C2×Q8—474no—
516C2×Q8—474no—
517C2×Q8—474no—
518C2×Q8—944no—
519C2×Q8—944no—
520C2×Q8—1882no—
521C2×Q8C2×C4×D4714yes—
522C22×C4—471no—
523C22×C4—471no—
524C22×C4—472no—
525C22×C4—474no—
526C22×C4—474no—
527C22×C4—472no—
528C22×C4—471no—
529C22×C4—471no—
530C22×C4—471no—
531C22×C4—471no—
532C22×C4—471no—
533C22×C4—474no—
534C22×C4—474no—
535C22×C4—944no—
536C22×C4—1882no—
537C22×C4C2×C4×D4711yescharacteristic
538C22×C4C2×C4×D4711yescharacteristic
539C22×C4C2×C4×D4711yescharacteristic
540C22×C4C2×C4×D4711yescharacteristic
541C22×C4C2×C4×D4711yescharacteristic
542C22×C4C2×C4×D4711yescharacteristic
543C22×C4C23×D4711yescharacteristic
544M16—4716no—
545M16—948no—
546C2×C8—22no—
547C2×C8—22no—
548C2×C8—22no—
549C2×C8—474no—
550C2×C8—472no—
551C2×C8—472no—
552C2×C8—472no—
553C2×C8—472no—
554C2×C8—948no—
555C2×C8—948no—
556C2×C8—942no—
557C2×C8—942no—
558C2×C8—942no—
559C2×C8Q8×D4714yes—
560C2×C8C23×D4712yes—
561C2×C8C23×D4712yes—
562C2×C8C23×D4712yes—
563C2×C8C23×D4712yes—
564C4⋊C4—474no—
565C4⋊C4—474no—
566C4⋊C4—474no—
567C4⋊C4—474no—
568C4⋊C4—474no—
569C4⋊C4—474no—
570C4⋊C4—474no—
571C4⋊C4—474no—
572C4⋊C4—474no—
573C4⋊C4—474no—
574C4⋊C4—474no—
575C4⋊C4—474no—
576C4⋊C4—474no—
577C4⋊C4C2×C4×D4714yes—
578C4⋊C4C2×C4×D4714yes—
579C4⋊C4C2×C4×D4714yes—
580C22⋊C4—474no—
581C22⋊C4—474no—
582C22⋊C4—474no—
583C22⋊C4—474no—
584C42—472no—
585C42—474no—
586C42—474no—
587C42—472no—
588C42—472no—
589C42—472no—
590C42—472no—
591C42—472no—
592C42C2×C4×D4712yes—
593C42C2×C4×D4712yes—
594C42C2×C4×D4712yes—
595C42C23×D4712yes—
596C42C23×D4712yes—
597C42C23×D4712yes—
598C23—474no—
599C23—472no—
600C23—942no—
601C23—942no—
602C23C22×C4×D4711yescharacteristic
603Q8—44no—
604Q8—948no—
605Q8—948no—
606Q8—1884no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—474no—
614C2×C4—474no—
615C2×C4—472no—
616C2×C4—472no—
617C2×C4—478no—
618C2×C4—474no—
619C2×C4—474no—
620C2×C4—472no—
621C2×C4—472no—
622C2×C4—472no—
623C2×C4—472no—
624C2×C4—472no—
625C2×C4—948no—
626C2×C4—942no—
627C2×C4—942no—
628C2×C4—942no—
629C2×C4—942no—
630C2×C4—942no—
631C2×C4—1884no—
632C2×C4C22×C4×D4712yes—
633C2×C4C22×C4×D4712yes—
634C2×C4C22×C4×D4712yes—
635C2×C4C22×C4×D4712yes—
636C2×C4C22×C4×D4712yes—
637C2×C4C22×C4×D4712yes—
638C2×C4C22×C4×D4711yescharacteristic
639C2×C4C2×Q8×D4712yes—
640C2×C4#41×D4712yes—
641C2×C4C24×D4711yescharacteristic
642C8—22no—
643C8—22no—
644C8—22no—
645C8—474no—
646C8—942no—
647C8—942no—
648C8—942no—
649C8C2×Q8×D4714yes—
650C22—474no—
651C22—942no—
652C22—942no—
653C22—948no—
654C22C4×Q8×D4712yes—
655C22#131×D4712yes—
656C22#1568988912yes—
657C22C23×C4×D4711yescharacteristic
658C4—22no—
659C4—22no—
660C4—22no—
661C4—22no—
662C4—22no—
663C4—22no—
664C4—474no—
665C4—474no—
666C4—942no—
667C4—942no—
668C4—942no—
669C4—942no—
670C4—942no—
671C4C4×Q8×D4712yes—
672C4C22×Q8×D4711yescharacteristic
673C4C2×#41×D4711yescharacteristic
674C2—944no—
675C2#2025233314yesdirect product factor
676C2C2×C4×Q8×D4711yescharacteristic
677C2C2×#131×D4711yescharacteristic
678C2C2×#1568988911yescharacteristic
subgroupG/H
centerC22×C4C23×D47
commutatorC22×C47C24×C4
FrattiniC2×C4C24×D47
FittingC2×C47×#446C2
socleC23×C47C23×C4
prime radicalC23×D47C22×C4
cosocleC2×C4×C47C25
hypercenterC2×#446D47
hypocenterC47C2×#2962
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C2×#446

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #20252333C2direct (N × H)
3. C2×#15689254C2semidirect
4. C2×#15689252C2semidirect
5. C2×#15689252C2semidirect
6. C2×#15689251C2semidirect
7. C2×#15689251C2semidirect
8. C2×C8×Dic94C2semidirect
9. C2×#15689247C2semidirect
16. C2×C47×#446C2semidirect
37. #15689254C22semidirect
38. #15689252C22semidirect
39. #15689252C22semidirect
40. #15689251C22semidirect
41. #15689251C22semidirect
42. C8×Dic94C22semidirect
43. #15689247C22semidirect
69. C47×#446C22semidirect
83. C2×#10625324Q8semidirect
255. #10625324C2×Q8semidirect
342. C2×#446D47semidirect
351. C2×C47#2962semidirect
382. #446C2×D47semidirect
415. C47C2×#2962semidirect
675. C2#20252333direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#156896772
#202523332
C2×#156892542
C2×#156892522
C2×#156892512
C2×C8×Dic942
C2×#156892472
C2×#156891482
C2×C4⋊C8×D472
C2×#156890802
C2×#156890772
C2×#156890752
C2×C47×#4462
C2×#296247